Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Rachel98

I don't really get this. Question: Use the rules for exponents and roots to prove that 512^2/3 = 16^3/2

  • one year ago
  • one year ago

  • This Question is Closed
  1. mjr632
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you mean a rigorous formal proof?

    • one year ago
  2. Rachel98
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't really know. This is what the question was and I don't get it.

    • one year ago
  3. mjr632
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you understand how to use logarithms?

    • one year ago
  4. Rachel98
    Best Response
    You've already chosen the best response.
    Medals 0

    No

    • one year ago
  5. mjr632
    Best Response
    You've already chosen the best response.
    Medals 0

    Ah, you will want to understand natural logarithms for this question, I can explain it.

    • one year ago
  6. mjr632
    Best Response
    You've already chosen the best response.
    Medals 0

    \[y = \log_b x\] \[x = b^y\]

    • one year ago
  7. mjr632
    Best Response
    You've already chosen the best response.
    Medals 0

    If we take the natural logarithm of \[512^{\frac{2}{3}}\] \[\frac{2}{3}\ln(512)\]

    • one year ago
  8. mjr632
    Best Response
    You've already chosen the best response.
    Medals 0

    We can pull the exponent out

    • one year ago
  9. Rachel98
    Best Response
    You've already chosen the best response.
    Medals 0

    So, is that a cube root? That we ended up with?

    • one year ago
  10. precal
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360950294527:dw|

    • one year ago
  11. precal
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360950347726:dw|

    • one year ago
  12. precal
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360950360574:dw|

    • one year ago
  13. precal
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360950390774:dw|

    • one year ago
  14. precal
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1360950432326:dw|

    • one year ago
  15. precal
    Best Response
    You've already chosen the best response.
    Medals 1

    yes they are both equivalent

    • one year ago
  16. Rachel98
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks, so much. That makes sense now.

    • one year ago
  17. precal
    Best Response
    You've already chosen the best response.
    Medals 1

    yw

    • one year ago
  18. precal
    Best Response
    You've already chosen the best response.
    Medals 1

    no need to use logs here

    • one year ago
  19. ghass1978
    Best Response
    You've already chosen the best response.
    Medals 1

    just using exponents :512=2^9 so 512^(2/3)=2^6 and 16^(3/2)=2^6 so both are equal

    • one year ago
  20. Rachel98
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks

    • one year ago
  21. precal
    Best Response
    You've already chosen the best response.
    Medals 1

    yw

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.